Answer by Larry R. Irwin for Move file to external hard drive sub-directory

Mount the device as /mnt/usb

Create a folder

mkdir -p  /mnt/usb/Backup/Dec_02_2016

Copy to the recently mounted device

cp -p /home/User_F_Readout/Downloads/Temp_Report_56_09242016.txt /mnt/usb/Backup/Dec_02_2016